Black Holes and Singularity Resolution in Higher Spin Gravity

We study the higher spin black holes in a truncated version of higher spin gravity in $AdS_3$. This theory contains only finite number of even spins s=2,4,...,2N. We mainly focus on the simplest case, so-called (Type I and II) spin ${\tilde 4}$ gravity, which contains only spin 2 and spin 4 fields. This spin ${\tilde 4}$ gravity is as simple as spin 3 gravity, thus provides another example to test various ideas on higher spin gravity. We find that the asymptotical symmetry of...

We study the propagation of scalar fields on various backgrounds in three dimensional higher spin gravity. Our main emphasis is on obtaining the bulk-boundary propagator, which can be efficiently computed using group theory and higher spin gauge symmetry and from which we can extract scalar two-point functions in the dual CFT. As an illustration, we obtain a simple closed form expression for the propagator in a particular spin-3 deformation of AdS_3. In the case of higher spi...

BTZ black hole is interpreted as exact solution of 3d higher spin gauge theory. Solutions for free massless fields in BTZ black hole background are constructed with the help of the star-product algebra formalism underlying the formulation of 3d higher spin theory. It is shown that a part of higher spin symmetries remains unbroken for special values of the BTZ parameters.

We examine the thermodynamic properties of recently constructed black hole solutions in SL(3,R) x SL(3,R) Chern-Simons theory in the presence of a chemical potential for spin-3 charge, which acts as an irrelevant deformation of the dual CFT with W_3 x W_3 symmetry. The smoothness or holonomy conditions admit four branches of solutions describing a flow between two AdS_3 backgrounds corresponding to two different CFTs. The dominant branch at low temperatures, connected to the ...

In the context of (2+1)--dimensional SL(N,R)\times SL(N,R) Chern-Simons theory we explore issues related to regularity and asymptotics on the solid torus, for stationary and circularly symmetric solutions. We display and solve all necessary conditions to ensure a regular metric and metric-like higher spin fields. We prove that holonomy conditions are necessary but not sufficient conditions to ensure regularity, and that Hawking conditions do not necessarily follow from them. ...

Higher spin gravity in three dimensions has explicit black holes solutions, carrying higher spin charge. We compute the free energy of a charged black hole from the holographic dual, a 2d CFT with extended conformal symmetry, and find exact agreement with the bulk thermodynamics. In the CFT, higher spin corrections to the free energy can be calculated at high temperature from correlation functions of W-algebra currents.

We review and extend some recent results concerning the analysis of spacetime singularities in four-dimensional higher spin gravity, summarizing how the coupling of the gravitational field to massless higher spins may provide resolution mechanisms. We elucidate such mechanisms at the level of curvature singularities and degenerate metrics in exact as well as linearized solutions to Vasiliev's equations. As a preamble, we review the underlying higher-spin algebra and its metap...

We consider the coupling of a symmetric spin-3 gauge field to three-dimensional gravity in a second order metric-like formulation. The action that corresponds to an SL(3,R) x SL(3,R) Chern-Simons theory in the frame-like formulation is identified to quadratic order in the spin-3 field. We apply our result to compute corrections to the area law for higher-spin black holes using Wald's entropy formula.

A review of recent investigations of black holes in higher curvature theories of gravity.

We study Lorentzian eternal black holes in the Chern-Simons sector of AdS$_3$ higher spin gravity. We probe such black holes using bulk Wilson lines and motivate new regularity conditions that must be obeyed by the bulk connections in order for the geometry to be consistent with an interpretation as a thermofield state in the dual CFT$_2$. We demonstrate that any higher spin black hole may be placed in a gauge that satisfies these conditions: this is the Chern-Simons analogue...